Related papers: R-local Delaunay inhibition model
The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the…
We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…
We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to…
Let $P$ be a set of $n$ points in $\mathrm{R}^2$, and let $\mathrm{DT}(P)$ denote its Euclidean Delaunay triangulation. We introduce the notion of an edge of $\mathrm{DT}(P)$ being {\it stable}. Defined in terms of a parameter $\alpha>0$, a…
We consider the Gibbs representation over space-time of non-equilibrium dynamics of Hamiltonian systems defined on a lattice with local interactions. We first write the corresponding action functional as a sum of local terms, defining a…
We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…
The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced wave instabilities for various local excitatory and…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
The generalized Gibbs-Duhem equation is obtained for systems with long-range interactions in $d$ spatial dimensions. We consider that particles in the system interact through a slowly decaying pair potential of the form $1/r^\nu$ with…
Well-posedness in $L_\infty$ of the nonlocal Gray-Scott model is studied for integrable kernels, along with the stability of the semi-trivial spatially homogeneous steady state. In addition, it is shown that the solutions to the nonlocal…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the…
We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the…
A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity.…
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not \textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian…
In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state…
In this paper, we aim to find the conditions for input-state stability (ISS) and incremental input-state stability ($\delta$ISS) of Gated Graph Neural Networks (GGNNs). We show that this recurrent version of Graph Neural Networks (GNNs) can…
We propose a real-space approach explaining and controlling the occurrence of edge-localized gap states between the spectral quasibands of binary tight binding chains with deterministic aperiodic long-range order. The framework is applied…
We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical…